How do you evaluate the definite integral by the limit definition given #int 6dx# from [4,10]?
This is the equivalent of drawing a rectangle whose boundaries are the line
This rectangle would therefore have a length of
Since the definite integral is in fact a measure of area, this is the answer.
Using the limit definition
The limit definition of a definite integral is
#=lim_(n->oo) sum_(i = 1)^n f (4+(6i)/n) xx 6/n#
#=lim_(n->oo) sum_(i = 1)^n 6 xx 6/n#
#=lim_(n->oo) sum_(i = 1)^n 36/n#
Use the formula
#=lim_(n-> oo) n(36)/n#
We integrate using the formula
We now rewrite in proper notation, and evaluate using the second fundamental theorem of calculus, which is that
Same answer as before, just using a different method.
Hopefully this helps!